Charles C. Beckner

Fast and optimal multiframe blind deconvolution algorithm for high-resolution ground-based imaging of space objects

We report a multiframe blind deconvolution algorithm that we have developed for imaging through the atmosphere. The algorithm has been parallelized to a significant degree for execution on high-performance computers, with an emphasis on distributed-memory systems so that it can be hosted on commodity clusters. As a result, image restorations can be obtained in seconds to minutes. We have compared and quantified the quality of its image restorations relative to the associated Cramér-Rao lower bounds (when they can be calculated). We describe the algorithm and its parallelization in detail, demonstrate the scalability of its parallelization across distributed-memory computer nodes, discuss the results of comparing sample variances of its output to the associated Cramér-Rao lower bounds, and present image restorations obtained by using data collected with ground-based telescopes.

Fundamental limits to noise reduction in images using support: benefits from deconvolution

The usefulness of support constraints to achieve noise reduction in images is analyzed here using an algorithm-independent Cramer-Rao bound approach. Recently, it has been shown that the amount of noise reduction achievable using support as a constraint is a function of the image-domain noise correlation properties. For image-domain delta-correlated noise sources (such as Poisson and CCD read noise), applying a support constraint does not reduce noise in the absence of deconvolution due to the lack of spatial correlation. However, when deconvolution is included in the image processing algorithm, the situation changes significantly because the deconvolution operation imposes correlations in the measurement noise. Here we present results for an invertible system blurring function showing how noise reduction occurs with support and deconvolution. In particular, we show that and explain why noise reduction preferentially occurs at the edges of the support constraint.

Implementation of a projection-on-constraints algorithm for beam intensity redistribution

Multi-Conjugate Adaptive-Optical (MCAO) systems have been proposed as a means of compensating both intensity and phase aberrations in a beam propagating through strong-scintillation environments. Progress made on implementing a MCAO system at the Starfire Optical Range (SOR), Air Force Research Laboratory, Kirtland AFB, is discussed. In previous work, it was shown that the First-stage Intensity Redistribution Experiment (FIRE) controlled and compensated wavefront intensity for static cases. As a secondary step toward controlling a two deformable mirror (DM) system, the FIRE experimental layout is used to examine another aspect of an MCAO system faster control of wavefront intensity. The FIRE experimental layout employs two wavefront sensors (WFS) and a single DM. One WFS is placed conjugate to the DM while the second WFS is located at a distance which produces a desired Fresnel number for the propagation between theWFSs. A modified Gerchberg- Saxton (GS) algorithm that propagates between image planes is employed for determining DM commands. The forward and back propagation portion of each GS iteration are computed in software. Using the GS solution, a control loop is closed on a WFS reconstructor in order to maintain beam shape in moving optical turbulence. The forward propagation phase pattern produced by the GS algorithm is tailored, via constraints, so that beam propagation along the path between the two WFSs produces a desired intensity profile and minimizes phase aberrations at the second WFS. In the next phase of MCAO development, a second DM will be added conjugate to the second WFS in order to correct the remaining phase aberrations.

Using mean-squared error to assess visual image quality

Conclusions about the usefulness of mean-squared error for predicting visual image quality are presented in this paper. A standard imaging model was employed that consisted of: an object, point spread function, and noise. Deconvolved reconstructions were recovered from blurred and noisy measurements formed using this model. Additionally, image reconstructions were regularized by classical Fourier-domain filters. These post-processing steps generated the basic components of mean-squared error: bias and pixel-by-pixel noise variances. Several Fourier domain regularization filters were employed so that a broad range of bias/variance tradeoffs could be analyzed. Results given in this paper show that mean-squared error is a reliable indicator of visual image quality only when the images being compared have approximately equal bias/variance ratios.

Achievability of Multi-Frame Blind Deconvolution Cramér-Rao Lower Bounds

The achievability of MFBD CRBs for both object and blurring functions using Fourier-domain metrics depend upon signal-to-noise ratios and the quality of the prior knowledge included in the reconstruction process

Evaluation of a Multi-frame Blind Deconvolution Algorithm Using Cramér-Rao Bounds

Sample statistics from a maximum-likelihood based multi-frame blind-deconvolution (MFBD) algorithm are compared with Cramer-Rao bound results in order to evaluate the noise reduction performance of the MFBD algorithm.

Intensity redistribution for multiconjugate adaptive optics

Multi-Conjugate Adaptive-Optical (MCAO) systems have been proposed as a means of compensating both intensity and phase aberrations in a beam propagating through strong-scintillation environments. Progress made on implementing a MCAO system at the Starfire Optical Range (SOR), Air Force Research Laboratory, Kirtland AFB, is discussed. As a preliminary step toward controlling a two deformable mirror (DM) system, the First-stage Intensity Redistribution Experiment (FIRE) examines one aspect of an MCAO system-control and compensation of wavefront intensity. Two wavefront sensors (WFS) and a single DM are employed for this experiment. One WFS is placed conjugate to the DM while the second WFS is located at a distance which produces a desired Fresnel number for the propagation between the WFSs. The WFS measurements are input to a Gerchberg-Saxton based control algorithm in order to determine the DM commands. The phase pattern introduced by the DM is chosen so propagation along the path between the two WFSs produces a desired intensity profile at the second WFS. The second WFS is also used to determine the accuracy of the intensity redistribution and measure its effects on the wavefront phase. In the next phase of MCAO development, a second DM will be added conjugate to the second WFS in order to correct the remaining phase aberrations. This paper presents the setup and operation for FIRE along with initial laboratory results.